Al48.18Cr22.78Fe4.04Si3

Liang, X.; Fan, C.; Wen, B.; Zhang, L.

doi:10.1107/S2414314625010399

inorganic compounds

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ISSN: 2414-3146

Volume 10| Part 11| November 2025| x251039

https://doi.org/10.1107/S2414314625010399

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Al_48.18Cr_22.78Fe_4.04Si₃

Xinyu Liang,^a Changzeng Fan,^a,^b ^* Bin Wen ^a and Lifeng Zhang ^a,^c

^aState Key Laboratory of Metastable Materials Science and Technology, Yanshan University, Qinhuangdao 066004, People's Republic of China, ^bHebei Key Lab for Optimizing Metal Product Technology and Performance, Yanshan University, Qinhuangdao 066004, People's Republic of China, and ^cSchool of Mechanical and Materials Engineering, North China University of Technology, Beijing 100144, People's Republic of China
^*Correspondence e-mail: [email protected]

Edited by S. Bernès, Benemérita Universidad Autónoma de Puebla, México (Received 12 August 2025; accepted 19 November 2025; online 21 November 2025)

A mixture with the initial chemical composition Al₅₉Cr₂₁Fe₁₀Si₁₀ was subjected to high-pressure sintering, resulting in the unexpected synthesis of an intermetallic compound with the composition Al_48.18Cr_22.78Fe_4.04Si₃, which adopts the Cr_0.88Fe_0.12Ga structure type in the space group R3m. Structural analysis indicates that Al, Cr and Fe jointly occupy a special position (Wyckoff site 18h), with refined site occupancy factors of 0.676 (6), 0.17 (2) and 0.16 (2), respectively. Cr and Fe share another special position (Wyckoff site 3b), with refined site occupancy factors of 0.60 (6) and 0.40 (6), respectively. Other atoms in the crystal (Al and Si) fully occupy their sites.

Keywords: crystal structure; high-pressure sintering; intermetallic; decagonal quasicrystal.

CCDC reference: 2504093

Structure description

Quaternary decagonal quasicrystals (DQC) have been discovered in a few systems, for example, Ga–Fe–Cu–Si, Ga–V–Ni–Si and Al–Mn–Fe–Ge. However, there have been far fewer detailed studies of the stability of quaternary DQCs and correspondingly, there is far less atomic-scale structural information. The quaternary Al–Cr–Fe–Si DQCs exhibit distinctive structural characteristics, thereby constituting a novel structural class of DQCs. Specifically, the presence of multiple types of 2-nm decagons exhibiting both perfect and destructive tenfold symmetry within Al–Cr–Fe–Si DQCs is noteworthy, as such a phenomenon is rarely observed in other DQCs. This observation is likely to generate considerable interest, as the 2-nm decagons constitute the most significant structural element of DQCs. Therefore, it is imperative that an exhaustive study of the thermodynamic stability and the corresponding atomic-scale structural information to be conducted.

Ma et al. (2018 , 2020 ) discovered the DQC Al₅₉Cr₂₁Fe₁₀Si₁₀ by melting the quaternary alloy Al₆₀Cr₂₀Fe₁₀Si₁₀ in an induction furnace under an argon atmosphere, using high-purity elements. The molten alloy was then poured into a graphite crucible in the furnace to form ingots. Some fragments of the ingots were sealed in vacuum tubes for heat treatment.

In the present study we synthesized a new γ-brass phase, namely Al_48.18Cr_22.78Fe_4.04Si₃ utilizing a high-temperature and high-pressure method based on the composition Al₅₉Cr₂₁Fe₁₀Si₁₀, as detailed in the Synthesis section. It is evident that the system under consideration shares many similarities with other systems with a similar structure. For example, Hu et al. (2021 ) found Al_8.6Mn_4.4 in the same space group [a = 12.6751 (13), c = 7.9137 (9) Å]; Ko et al. (2010 ) found Cr_0.88Fe_0.12Ga [a = b = 12.6431 (18), c = 7.8985 (16) Å]. The structure of Al_48.18Cr_22.78Fe_4.04Si₃ is similar to that of Cr_0.88Fe_0.12Ga; in the former, Al, Cr and Fe share a special position (Wyckoff position 18h in the space group R $[\overline{3}]$ m), with refined site occupancy factors of 0.676 (6), 0.17 (2) and 0.16 (2), while in the latter, Fe and Cr share this position, with refined site occupancy factors of 0.26 and 0.74 (Ko et al., 2010). However, no reports are available so far for the quaternary alloy phase of Al–Cr–Fe–Si with such a structure.

In this study, we refined the crystal structure model of Al_48.18Cr_22.78Fe_4.04Si₃ based on single-crystal X-ray diffraction data. Its chemical composition is in accordance with EDX measurements; various attempts are made with different results at each position (see the supporting information). The crystal structure and parts thereof are shown in Figs. 1 and 2,

Figure 1
The crystal structure of Al_48.18Cr_22.78Fe_4.04Si₃. The icosahedra centred on Si1 are emphasized.

Figure 2
(a) The icosahedra formed around the Si1 atom at the 3a site; (b) the environment of the Si1 atom with displacement ellipsoids given at the 99% probability level. [Symmetry codes: (i) x − $[{2\over 3}]$ , y − $[{1\over 3}]$ , z − $[{1\over 3}]$ ; (ii) −x + y + $[{1\over 3}]$ , −x + $[{2\over 3}]$ , z − $[{1\over 3}]$ ; (vii) −x + y, −x, z; (viii) −y, x − y, z; (xiii) x − y − $[{1\over 3}]$ , x − $[{2\over 3}]$ , −z + $[{1\over 3}]$ ; (xiv) −x + $[{2\over 3}]$ , −y + $[{1\over 3}]$ , −z + $[{1\over 3}]$ ; (xvii) x − y, x, −z; (xviii) −x, −y, −z; (xix) y, −x + y, −z.]

Synthesis and crystallization

The high-purity elements Al (indicated purity 99.8%; 0.4519 g), Cr (indicated purity 99.95%; 0.3099 g), Fe (indicated purity 99.9%; 0.1585 g), and Si (indicated purity 99.9%; 0.0797 g) were uniformly mixed in a stoichiometric ratio of 59:21:10:10 and thoroughly ground in an agate mortar. The mixed powder was placed into a cemented carbide grinding mould of 5 mm diameter and pressed into a block under a pressure of approximately 5 MPa for 3 min. A cylindrical block was obtained without deformations or cracks. The experimental details of high-pressure sintering using a six-anvil high-temperature high-pressure device can be consulted in Liu & Fan (2018 ).

In the current work, the prepared cylindrical block mixture was pressurized up to 6 GPa and heated to 1473 K for 30 min., cooled to 1173 K, held at that temperature for 60 min., and then rapidly cooled down to room temperature. A fragment was selected and mounted on a glass fibre for single-crystal X-ray diffraction measurements.

Refinement

Table 1 shows the details of data collection and structural refinement. The labelling scheme and atomic coordinates of Al_48.18Cr_22.78Fe_4.04Si₃ were adapted from Cr_0.88Fe_0.12Ga for better comparison. One site is co-occupied by Al, Cr and Fe atoms (Al1/Cr3/Fe1), and site occupancies were refined to 0.676 (6) for Al, 0.17 (2) for Cr and 0.16 (2) for Fe. Another site is co-occupied by Cr and Fe (Cr2/Fe2), and site occupancies were refined to 0.60 (6) for Cr and 0.40 (6) for Fe. Atoms sharing the same position were constrained to have identical coordinates and displacement parameters. The maximum and minimum residual electron densities in the last difference map are located 1.18 Å from atom Si1 and 0.75 Å from atom Al3, respectively.

Table 1
Experimental details

Crystal data
Chemical formula	Al_48.18Cr_22.78Fe_4.04Si₃
M_r	2794.43
Crystal system, space group	Trigonal, R $[\overline{3}]$ m:H
Temperature (K)	296
a, c (Å)	12.5478 (9), 7.9296 (9)
V (Å³)	1081.2 (2)
Z	1
Radiation type	Mo Kα
μ (mm⁻¹)	7.85
Crystal size (mm)	0.08 × 0.06 × 0.06

Data collection
Diffractometer	Bruker D8 Venture Photon 100 CMOS
Absorption correction	Multi-scan (SADABS; Krause et al., 2015 )
T_min, T_max	0.574, 0.746
No. of measured, independent and observed [I > 2σ(I)] reflections	10693, 417, 338
R_int	0.099
(sin θ/λ)_max (Å⁻¹)	0.715

Refinement
R[F² > 2σ(F²)], wR(F²), S	0.031, 0.047, 1.13
No. of reflections	417
No. of parameters	32
No. of restraints	1
Δρ_max, Δρ_min (e Å⁻³)	0.55, −1.04
Computer programs: APEX5 and SAINT (Bruker, 2023 ), SHELXT2018/2 (Sheldrick, 2015a ), SHELXL2018/3 (Sheldrick, 2015b ), DIAMOND (Brandenburg & Putz, 2017 ) and publCIF (Westrip, 2010 ).

Structural data

CCDC reference: 2504093

Crystal structure: contains datablock I. DOI: https://doi.org/10.1107/S2414314625010399/bh4100sup1.cif

Figures and supplementary materials. DOI: https://doi.org/10.1107/S2414314625010399/bh4100sup3.zip

Structure factors: contains datablock I. DOI: https://doi.org/10.1107/S2414314625010399/bh4100Isup4.hkl

checkCIF report

Computing details top

Aluminium chromium iron silicide top

Crystal data top

Al_48.18Cr_22.78Fe_4.04Si₃	D_x = 4.292 Mg m⁻³
M_r = 2794.43	Mo Kα radiation, λ = 0.71073 Å
Trigonal, R3m:H	Cell parameters from 2885 reflections
a = 12.5478 (9) Å	θ = 3.2–28.5°
c = 7.9296 (9) Å	µ = 7.85 mm⁻¹
V = 1081.2 (2) Å³	T = 296 K
Z = 1	Lump, grey
F(000) = 1320	0.08 × 0.06 × 0.06 mm

Data collection top

Bruker D8 Venture Photon 100 CMOS diffractometer	338 reflections with I > 2σ(I)
phi and ω scans	R_int = 0.099
Absorption correction: multi-scan (SADABS; Krause et al., 2015)	θ_max = 30.5°, θ_min = 3.2°
T_min = 0.574, T_max = 0.746	h = −17→17
10693 measured reflections	k = −17→17
417 independent reflections	l = −11→11

Refinement top

Refinement on F²	1 restraint
Least-squares matrix: full	Primary atom site location: dual
R[F² > 2σ(F²)] = 0.031	Secondary atom site location: difference Fourier map
wR(F²) = 0.047	w = 1/[σ²(F_o²) + (0.0136P)² + 4.4686P] where P = (F_o² + 2F_c²)/3
S = 1.13	(Δ/σ)_max = 0.004
417 reflections	Δρ_max = 0.55 e Å⁻³
32 parameters	Δρ_min = −1.03 e Å⁻³

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å²) top

	x	y	z	U_iso*/U_eq	Occ. (<1)
Al1	−0.07243 (4)	0.07243 (4)	0.24743 (10)	0.0082 (3)	0.676 (6)
Al2	0.37822 (10)	0.37822 (10)	0.500000	0.0096 (3)
Al3	0.23539 (11)	0.11769 (5)	0.57349 (15)	0.0108 (3)
Cr3	−0.07243 (4)	0.07243 (4)	0.24743 (10)	0.0082 (3)	0.17 (2)
Si1	0.000000	0.000000	0.000000	0.0127 (6)
Fe1	−0.07243 (4)	0.07243 (4)	0.24743 (10)	0.0082 (3)	0.16 (2)
Cr1	0.43537 (5)	0.21768 (3)	0.40484 (7)	0.00680 (18)
Cr2	0.000000	0.000000	0.500000	0.0035 (4)	0.60 (6)
Fe2	0.000000	0.000000	0.500000	0.0035 (4)	0.40 (6)

Atomic displacement parameters (Å²) top

	U¹¹	U²²	U³³	U¹²	U¹³	U²³
Al1	0.0089 (4)	0.0089 (4)	0.0056 (4)	0.0033 (4)	−0.00109 (17)	0.00109 (17)
Al2	0.0107 (5)	0.0107 (5)	0.0092 (5)	0.0068 (5)	0.0011 (2)	−0.0011 (2)
Al3	0.0066 (6)	0.0125 (5)	0.0114 (6)	0.0033 (3)	−0.0012 (5)	−0.0006 (2)
Cr3	0.0089 (4)	0.0089 (4)	0.0056 (4)	0.0033 (4)	−0.00109 (17)	0.00109 (17)
Si1	0.0162 (9)	0.0162 (9)	0.0057 (12)	0.0081 (5)	0.000	0.000
Fe1	0.0089 (4)	0.0089 (4)	0.0056 (4)	0.0033 (4)	−0.00109 (17)	0.00109 (17)
Cr1	0.0084 (3)	0.0068 (3)	0.0057 (3)	0.00420 (17)	0.0003 (2)	0.00016 (12)
Cr2	0.0035 (5)	0.0035 (5)	0.0036 (7)	0.0017 (3)	0.000	0.000
Fe2	0.0035 (5)	0.0035 (5)	0.0036 (7)	0.0017 (3)	0.000	0.000

Geometric parameters (Å, º) top

Al1—Si1	2.5154 (9)	Al2—Al2^ix	2.8175 (8)
Al1—Fe2	2.5473 (8)	Al2—Al3	2.8947 (12)
Al1—Cr2	2.5473 (8)	Al2—Al3^iv	2.8948 (12)
Al1—Cr1ⁱ	2.6048 (7)	Al3—Cr1	2.5516 (13)
Al1—Cr1ⁱⁱ	2.6048 (7)	Al3—Al3^xi	2.591 (2)
Al1—Al2ⁱ	2.6344 (10)	Al3—Fe2	2.6234 (12)
Al1—Al2ⁱⁱⁱ	2.6344 (10)	Al3—Cr2	2.6234 (12)
Al1—Al3^iv	2.6478 (11)	Al3—Al3^iv	2.8108 (14)
Al1—Al3^v	2.6478 (11)	Al3—Al3^xii	2.8108 (14)
Al1—Cr1^vi	2.6979 (10)	Al3—Cr1^xi	2.8154 (14)
Al1—Al1^vii	2.7264 (16)	Si1—Cr1^xiii	2.5766 (6)
Al1—Al1^viii	2.7264 (16)	Si1—Cr1ⁱⁱ	2.5766 (6)
Al2—Cr1^iv	2.5663 (4)	Si1—Cr1ⁱ	2.5766 (6)
Al2—Cr1	2.5663 (4)	Si1—Cr1^xiv	2.5766 (6)
Al2—Cr1^ix	2.6705 (8)	Cr1—Cr1^x	2.7575 (7)
Al2—Cr1^x	2.6705 (8)	Cr1—Cr1^xv	2.7576 (7)
Al2—Al2ⁱⁱ	2.8175 (8)

Si1—Al1—Fe2	103.10 (3)	Al1^xix—Si1—Cr1^xiii	116.03 (2)
Si1—Al1—Cr2	103.10 (3)	Al1^viii—Si1—Cr1^xiii	63.97 (2)
Si1—Al1—Cr1ⁱ	60.40 (2)	Al1—Si1—Cr1^xiii	118.481 (11)
Cr2—Al1—Cr1ⁱ	110.23 (2)	Al1^xvii—Si1—Cr1ⁱⁱ	118.482 (11)
Si1—Al1—Cr1ⁱⁱ	60.40 (2)	Al1^vii—Si1—Cr1ⁱⁱ	61.518 (11)
Fe2—Al1—Cr1ⁱⁱ	110.23 (2)	Al1^xviii—Si1—Cr1ⁱⁱ	118.481 (11)
Cr2—Al1—Cr1ⁱⁱ	110.23 (2)	Al1^xix—Si1—Cr1ⁱⁱ	63.97 (2)
Cr1ⁱ—Al1—Cr1ⁱⁱ	113.37 (4)	Al1^viii—Si1—Cr1ⁱⁱ	116.03 (2)
Si1—Al1—Al2ⁱ	107.27 (3)	Al1—Si1—Cr1ⁱⁱ	61.519 (11)
Cr2—Al1—Al2ⁱ	132.19 (3)	Cr1^xiii—Si1—Cr1ⁱⁱ	180.0
Cr1ⁱ—Al1—Al2ⁱ	58.65 (2)	Al1^xvii—Si1—Cr1ⁱ	63.97 (2)
Cr1ⁱⁱ—Al1—Al2ⁱ	116.70 (4)	Al1^vii—Si1—Cr1ⁱ	116.03 (2)
Si1—Al1—Al2ⁱⁱⁱ	107.27 (3)	Al1^xviii—Si1—Cr1ⁱ	118.481 (11)
Cr2—Al1—Al2ⁱⁱⁱ	132.19 (3)	Al1^xix—Si1—Cr1ⁱ	118.482 (11)
Cr1ⁱ—Al1—Al2ⁱⁱⁱ	116.70 (4)	Al1^viii—Si1—Cr1ⁱ	61.518 (11)
Cr1ⁱⁱ—Al1—Al2ⁱⁱⁱ	58.65 (2)	Al1—Si1—Cr1ⁱ	61.519 (11)
Al2ⁱ—Al1—Al2ⁱⁱⁱ	70.91 (5)	Cr1^xiii—Si1—Cr1ⁱ	64.698 (9)
Si1—Al1—Al3^iv	110.40 (3)	Cr1ⁱⁱ—Si1—Cr1ⁱ	115.302 (9)
Cr2—Al1—Al3^iv	60.62 (3)	Al1^xvii—Si1—Cr1^xiv	116.03 (2)
Cr1ⁱ—Al1—Al3^iv	166.60 (4)	Al1^vii—Si1—Cr1^xiv	63.97 (2)
Cr1ⁱⁱ—Al1—Al3^iv	64.82 (3)	Al1^xviii—Si1—Cr1^xiv	61.519 (11)
Al2ⁱ—Al1—Al3^iv	134.61 (4)	Al1^xix—Si1—Cr1^xiv	61.518 (11)
Al2ⁱⁱⁱ—Al1—Al3^iv	74.44 (3)	Al1^viii—Si1—Cr1^xiv	118.482 (11)
Si1—Al1—Al3^v	110.40 (3)	Al1—Si1—Cr1^xiv	118.481 (11)
Cr2—Al1—Al3^v	60.62 (3)	Cr1^xiii—Si1—Cr1^xiv	115.302 (9)
Cr1ⁱ—Al1—Al3^v	64.82 (3)	Cr1ⁱⁱ—Si1—Cr1^xiv	64.698 (9)
Cr1ⁱⁱ—Al1—Al3^v	166.60 (4)	Cr1ⁱ—Si1—Cr1^xiv	180.000 (16)
Al2ⁱ—Al1—Al3^v	74.44 (3)	Al3—Cr1—Al2^xii	68.89 (3)
Al2ⁱⁱⁱ—Al1—Al3^v	134.61 (4)	Al3—Cr1—Al2	68.89 (3)
Al3^iv—Al1—Al3^v	113.57 (6)	Al2^xii—Cr1—Al2	135.23 (5)
Si1—Al1—Cr1^vi	59.12 (2)	Al3—Cr1—Si1^xvi	161.11 (3)
Cr2—Al1—Cr1^vi	162.21 (4)	Al2^xii—Cr1—Si1^xvi	107.50 (3)
Cr1ⁱ—Al1—Cr1^vi	62.639 (19)	Al2—Cr1—Si1^xvi	107.50 (3)
Cr1ⁱⁱ—Al1—Cr1^vi	62.639 (19)	Al3—Cr1—Al1^ix	106.49 (3)
Al2ⁱ—Al1—Cr1^vi	60.09 (2)	Al2^xii—Cr1—Al1^ix	61.25 (3)
Al2ⁱⁱⁱ—Al1—Cr1^vi	60.09 (2)	Al2—Cr1—Al1^ix	119.13 (3)
Al3^iv—Al1—Cr1^vi	122.79 (3)	Si1^xvi—Cr1—Al1^ix	58.08 (2)
Al3^v—Al1—Cr1^vi	122.79 (3)	Al3—Cr1—Al1^xvi	106.49 (3)
Si1—Al1—Al1^vii	57.184 (16)	Al2^xii—Cr1—Al1^xvi	119.13 (3)
Fe2—Al1—Al1^vii	57.646 (16)	Al2—Cr1—Al1^xvi	61.25 (3)
Cr2—Al1—Al1^vii	57.646 (16)	Si1^xvi—Cr1—Al1^xvi	58.08 (2)
Cr1ⁱ—Al1—Al1^vii	108.20 (2)	Al1^ix—Cr1—Al1^xvi	63.11 (4)
Cr1ⁱⁱ—Al1—Al1^vii	58.44 (2)	Al3—Cr1—Al2ⁱⁱ	90.98 (3)
Al2ⁱ—Al1—Al1^vii	164.434 (19)	Al2^xii—Cr1—Al2ⁱⁱ	129.54 (2)
Al2ⁱⁱⁱ—Al1—Al1^vii	112.54 (2)	Al2—Cr1—Al2ⁱⁱ	65.06 (3)
Al3^iv—Al1—Al1^vii	59.01 (2)	Si1^xvi—Cr1—Al2ⁱⁱ	104.440 (18)
Al3^v—Al1—Al1^vii	108.77 (3)	Al1^ix—Cr1—Al2ⁱⁱ	162.44 (3)
Cr1^vi—Al1—Al1^vii	107.55 (2)	Al1^xvi—Cr1—Al2ⁱⁱ	110.76 (3)
Si1—Al1—Al1^viii	57.184 (16)	Al3—Cr1—Al2^xv	90.98 (3)
Cr2—Al1—Al1^viii	57.646 (16)	Al2^xii—Cr1—Al2^xv	65.06 (3)
Cr1ⁱ—Al1—Al1^viii	58.44 (2)	Al2—Cr1—Al2^xv	129.54 (2)
Cr1ⁱⁱ—Al1—Al1^viii	108.20 (2)	Si1^xvi—Cr1—Al2^xv	104.441 (18)
Al2ⁱ—Al1—Al1^viii	112.54 (2)	Al1^ix—Cr1—Al2^xv	110.76 (3)
Al2ⁱⁱⁱ—Al1—Al1^viii	164.434 (19)	Al1^xvi—Cr1—Al2^xv	162.44 (3)
Al3^iv—Al1—Al1^viii	108.77 (3)	Al2ⁱⁱ—Cr1—Al2^xv	69.81 (5)
Al3^v—Al1—Al1^viii	59.01 (2)	Al3—Cr1—Al1^xx	141.98 (4)
Cr1^vi—Al1—Al1^viii	107.55 (2)	Al2^xii—Cr1—Al1^xx	111.094 (17)
Al1^vii—Al1—Al1^viii	60.0	Al2—Cr1—Al1^xx	111.092 (17)
Cr1^iv—Al2—Cr1	150.72 (6)	Si1^xvi—Cr1—Al1^xx	56.91 (2)
Cr1^iv—Al2—Al1^xvi	142.35 (3)	Al1^ix—Cr1—Al1^xx	105.74 (3)
Cr1—Al2—Al1^xvi	60.10 (2)	Al1^xvi—Cr1—Al1^xx	105.74 (3)
Cr1^iv—Al2—Al1ⁱⁱⁱ	60.10 (2)	Al2ⁱⁱ—Cr1—Al1^xx	58.77 (2)
Cr1—Al2—Al1ⁱⁱⁱ	142.35 (3)	Al2^xv—Cr1—Al1^xx	58.77 (2)
Al1^xvi—Al2—Al1ⁱⁱⁱ	109.09 (5)	Al3—Cr1—Cr1^x	127.136 (8)
Cr1^iv—Al2—Cr1^ix	63.51 (2)	Al2^xii—Cr1—Cr1^x	163.97 (3)
Cr1—Al2—Cr1^ix	137.33 (3)	Al2—Cr1—Cr1^x	60.09 (2)
Al1^xvi—Al2—Cr1^ix	79.57 (3)	Si1^xvi—Cr1—Cr1^x	57.649 (5)
Al1ⁱⁱⁱ—Al2—Cr1^ix	61.13 (3)	Al1^ix—Cr1—Cr1^x	109.35 (2)
Cr1^iv—Al2—Cr1^x	137.33 (3)	Al1^xvi—Cr1—Cr1^x	60.33 (2)
Cr1—Al2—Cr1^x	63.51 (2)	Al2ⁱⁱ—Cr1—Cr1^x	56.40 (2)
Al1^xvi—Al2—Cr1^x	61.13 (3)	Al2^xv—Cr1—Cr1^x	110.49 (4)
Al1ⁱⁱⁱ—Al2—Cr1^x	79.57 (3)	Al1^xx—Cr1—Cr1^x	57.03 (2)
Cr1^ix—Al2—Cr1^x	110.19 (5)	Al3—Cr1—Cr1^xv	127.134 (8)
Cr1^iv—Al2—Al2ⁱⁱ	111.077 (13)	Al2^xii—Cr1—Cr1^xv	60.09 (2)
Cr1—Al2—Al2ⁱⁱ	59.25 (3)	Al2—Cr1—Cr1^xv	163.97 (3)
Al1^xvi—Al2—Al2ⁱⁱ	105.509 (18)	Si1^xvi—Cr1—Cr1^xv	57.652 (5)
Al1ⁱⁱⁱ—Al2—Al2ⁱⁱ	94.62 (3)	Al1^ix—Cr1—Cr1^xv	60.34 (2)
Cr1^ix—Al2—Al2ⁱⁱ	155.09 (5)	Al1^xvi—Cr1—Cr1^xv	109.35 (2)
Cr1^x—Al2—Al2ⁱⁱ	55.681 (11)	Al2ⁱⁱ—Cr1—Cr1^xv	110.49 (4)
Cr1^iv—Al2—Al2^ix	59.25 (3)	Al2^xv—Cr1—Cr1^xv	56.40 (2)
Cr1—Al2—Al2^ix	111.078 (13)	Al1^xx—Cr1—Cr1^xv	57.03 (2)
Al1^xvi—Al2—Al2^ix	94.62 (3)	Cr1^x—Cr1—Cr1^xv	104.26 (3)
Al1ⁱⁱⁱ—Al2—Al2^ix	105.509 (18)	Al3—Cr1—Al3^xi	57.49 (4)
Cr1^ix—Al2—Al2^ix	55.681 (11)	Al2^xii—Cr1—Al3^xi	72.675 (14)
Cr1^x—Al2—Al2^ix	155.09 (5)	Al2—Cr1—Al3^xi	72.673 (14)
Al2ⁱⁱ—Al2—Al2^ix	145.10 (7)	Si1^xvi—Cr1—Al3^xi	103.62 (3)
Cr1^iv—Al2—Al3	97.30 (4)	Al1^ix—Cr1—Al3^xi	58.33 (3)
Cr1—Al2—Al3	55.32 (3)	Al1^xvi—Cr1—Al3^xi	58.33 (3)
Al1^xvi—Al2—Al3	96.58 (3)	Al2ⁱⁱ—Cr1—Al3^xi	134.48 (3)
Al1ⁱⁱⁱ—Al2—Al3	154.10 (4)	Al2^xv—Cr1—Al3^xi	134.48 (3)
Cr1^ix—Al2—Al3	122.77 (3)	Al1^xx—Cr1—Al3^xi	160.53 (4)
Cr1^x—Al2—Al3	117.33 (3)	Cr1^x—Cr1—Al3^xi	114.73 (3)
Al2ⁱⁱ—Al2—Al3	81.39 (5)	Cr1^xv—Cr1—Al3^xi	114.74 (3)
Al2^ix—Al2—Al3	68.01 (3)	Al1^xii—Cr2—Al1^viii	180.0
Cr1^iv—Al2—Al3^iv	55.32 (3)	Al1^xii—Cr2—Al1^v	64.71 (3)
Cr1—Al2—Al3^iv	97.30 (4)	Al1^viii—Cr2—Al1^v	115.29 (3)
Al1^xvi—Al2—Al3^iv	154.09 (4)	Al1^xii—Cr2—Al1^iv	64.71 (3)
Al1ⁱⁱⁱ—Al2—Al3^iv	96.58 (3)	Al1^viii—Cr2—Al1^iv	115.29 (3)
Cr1^ix—Al2—Al3^iv	117.33 (3)	Al1^v—Cr2—Al1^iv	64.71 (3)
Cr1^x—Al2—Al3^iv	122.77 (3)	Al1^xii—Cr2—Al1^vii	115.29 (3)
Al2ⁱⁱ—Al2—Al3^iv	68.01 (3)	Al1^viii—Cr2—Al1^vii	64.71 (3)
Al2^ix—Al2—Al3^iv	81.39 (5)	Al1^v—Cr2—Al1^vii	115.29 (3)
Al3—Al2—Al3^iv	58.09 (5)	Al1^iv—Cr2—Al1^vii	180.0
Cr1—Al3—Al3^xi	66.38 (5)	Al1^xii—Cr2—Al1	115.29 (3)
Cr1—Al3—Fe2	135.56 (5)	Al1^viii—Cr2—Al1	64.71 (3)
Al3^xi—Al3—Fe2	158.07 (8)	Al1^v—Cr2—Al1	180.0
Cr1—Al3—Cr2	135.56 (5)	Al1^iv—Cr2—Al1	115.29 (3)
Al3^xi—Al3—Cr2	158.07 (8)	Al1^vii—Cr2—Al1	64.71 (3)
Cr1—Al3—Al1^xii	148.29 (3)	Al1^xii—Cr2—Al3^v	118.42 (2)
Al3^xi—Al3—Al1^xii	104.10 (6)	Al1^viii—Cr2—Al3^v	61.58 (2)
Fe2—Al3—Al1^xii	57.79 (3)	Al1^v—Cr2—Al3^v	118.42 (2)
Cr2—Al3—Al1^xii	57.79 (3)	Al1^iv—Cr2—Al3^v	64.67 (3)
Cr1—Al3—Al1^v	148.29 (3)	Al1^vii—Cr2—Al3^v	115.33 (3)
Al3^xi—Al3—Al1^v	104.10 (6)	Al1—Cr2—Al3^v	61.58 (2)
Cr2—Al3—Al1^v	57.79 (3)	Al1^xii—Cr2—Al3^iv	64.67 (3)
Al1^xii—Al3—Al1^v	61.97 (5)	Al1^viii—Cr2—Al3^iv	115.33 (3)
Cr1—Al3—Al1^vii	79.23 (4)	Al1^v—Cr2—Al3^iv	118.42 (2)
Al3^xi—Al3—Al1^vii	145.60 (8)	Al1^iv—Cr2—Al3^iv	118.42 (2)
Fe2—Al3—Al1^vii	56.33 (3)	Al1^vii—Cr2—Al3^iv	61.58 (2)
Cr2—Al3—Al1^vii	56.33 (3)	Al1—Cr2—Al3^iv	61.58 (2)
Al1^xii—Al3—Al1^vii	105.27 (4)	Al3^v—Cr2—Al3^iv	115.213 (18)
Al1^v—Al3—Al1^vii	105.27 (4)	Al1^xii—Cr2—Al3^vii	115.33 (3)
Cr1—Al3—Al3^iv	99.80 (4)	Al1^viii—Cr2—Al3^vii	64.67 (3)
Al3^xi—Al3—Al3^iv	127.604 (15)	Al1^v—Cr2—Al3^vii	61.58 (2)
Cr2—Al3—Al3^iv	57.606 (9)	Al1^iv—Cr2—Al3^vii	61.58 (2)
Al1^xii—Al3—Al3^iv	60.81 (3)	Al1^vii—Cr2—Al3^vii	118.42 (2)
Al1^v—Al3—Al3^iv	108.89 (3)	Al1—Cr2—Al3^vii	118.42 (2)
Al1^vii—Al3—Al3^iv	56.68 (4)	Al3^v—Cr2—Al3^vii	64.787 (18)
Cr1—Al3—Al3^xii	99.80 (4)	Al3^iv—Cr2—Al3^vii	180.0
Al3^xi—Al3—Al3^xii	127.606 (15)	Al1^xii—Cr2—Al3^viii	61.58 (2)
Fe2—Al3—Al3^xii	57.606 (9)	Al1^viii—Cr2—Al3^viii	118.42 (2)
Cr2—Al3—Al3^xii	57.606 (9)	Al1^v—Cr2—Al3^viii	115.33 (3)
Al1^xii—Al3—Al3^xii	108.89 (3)	Al1^iv—Cr2—Al3^viii	61.58 (2)
Al1^v—Al3—Al3^xii	60.81 (3)	Al1^vii—Cr2—Al3^viii	118.42 (2)
Al1^vii—Al3—Al3^xii	56.68 (4)	Al1—Cr2—Al3^viii	64.67 (3)
Al3^iv—Al3—Al3^xii	104.01 (5)	Al3^v—Cr2—Al3^viii	64.787 (18)
Cr1—Al3—Cr1^xi	122.51 (4)	Al3^iv—Cr2—Al3^viii	64.787 (18)
Al3^xi—Al3—Cr1^xi	56.13 (4)	Al3^vii—Cr2—Al3^viii	115.213 (18)
Cr2—Al3—Cr1^xi	101.93 (4)	Al1^xii—Fe2—Al1^viii	180.0
Al1^xii—Al3—Cr1^xi	56.85 (3)	Al1^xii—Fe2—Al1^v	64.71 (3)
Al1^v—Al3—Cr1^xi	56.85 (3)	Al1^viii—Fe2—Al1^v	115.29 (3)
Al1^vii—Al3—Cr1^xi	158.26 (5)	Al1^xii—Fe2—Al1^iv	64.71 (3)
Al3^iv—Al3—Cr1^xi	114.04 (5)	Al1^viii—Fe2—Al1^iv	115.29 (3)
Al3^xii—Al3—Cr1^xi	114.04 (5)	Al1^v—Fe2—Al1^iv	64.71 (3)
Cr1—Al3—Al2^xii	55.79 (2)	Al1^xii—Fe2—Al1^vii	115.29 (3)
Al3^xi—Al3—Al2^xii	70.99 (3)	Al1^viii—Fe2—Al1^vii	64.71 (3)
Fe2—Al3—Al2^xii	118.56 (3)	Al1^v—Fe2—Al1^vii	115.29 (3)
Cr2—Al3—Al2^xii	118.56 (3)	Al1^iv—Fe2—Al1^vii	180.0
Al1^xii—Al3—Al2^xii	152.70 (4)	Al1^xii—Fe2—Al1	115.29 (3)
Al1^v—Al3—Al2^xii	92.55 (2)	Al1^viii—Fe2—Al1	64.71 (3)
Al1^vii—Al3—Al2^xii	90.15 (3)	Al1^v—Fe2—Al1	180.0
Al3^iv—Al3—Al2^xii	143.76 (7)	Al1^iv—Fe2—Al1	115.29 (3)
Al3^xii—Al3—Al2^xii	60.95 (2)	Al1^vii—Fe2—Al1	64.71 (3)
Cr1^xi—Al3—Al2^xii	102.11 (3)	Al1^xii—Fe2—Al3^v	118.42 (2)
Cr1—Al3—Al2	55.79 (2)	Al1^viii—Fe2—Al3^v	61.58 (2)
Al3^xi—Al3—Al2	70.99 (3)	Al1^v—Fe2—Al3^v	118.42 (2)
Fe2—Al3—Al2	118.56 (3)	Al1^iv—Fe2—Al3^v	64.67 (3)
Cr2—Al3—Al2	118.56 (3)	Al1^vii—Fe2—Al3^v	115.33 (3)
Al1^xii—Al3—Al2	92.55 (2)	Al1—Fe2—Al3^v	61.58 (2)
Al1^v—Al3—Al2	152.70 (4)	Al1^xii—Fe2—Al3^iv	64.67 (3)
Al1^vii—Al3—Al2	90.15 (3)	Al1^viii—Fe2—Al3^iv	115.33 (3)
Al3^iv—Al3—Al2	60.95 (2)	Al1^v—Fe2—Al3^iv	118.42 (2)
Al3^xii—Al3—Al2	143.76 (7)	Al1^iv—Fe2—Al3^iv	118.42 (2)
Cr1^xi—Al3—Al2	102.11 (3)	Al1^vii—Fe2—Al3^iv	61.58 (2)
Al2^xii—Al3—Al2	110.12 (4)	Al1—Fe2—Al3^iv	61.58 (2)
Al1^xvii—Si1—Al1^vii	180.000 (16)	Al3^v—Fe2—Al3^iv	115.213 (18)
Al1^xvii—Si1—Al1^xviii	65.63 (3)	Al1^xii—Fe2—Al3^vii	115.33 (3)
Al1^vii—Si1—Al1^xviii	114.37 (3)	Al1^viii—Fe2—Al3^vii	64.67 (3)
Al1^xvii—Si1—Al1^xix	65.63 (3)	Al1^v—Fe2—Al3^vii	61.58 (2)
Al1^vii—Si1—Al1^xix	114.37 (3)	Al1^iv—Fe2—Al3^vii	61.58 (2)
Al1^xviii—Si1—Al1^xix	65.63 (3)	Al1^vii—Fe2—Al3^vii	118.42 (2)
Al1^xvii—Si1—Al1^viii	114.37 (3)	Al1—Fe2—Al3^vii	118.42 (2)
Al1^vii—Si1—Al1^viii	65.63 (3)	Al3^v—Fe2—Al3^vii	64.787 (18)
Al1^xviii—Si1—Al1^viii	114.37 (3)	Al3^iv—Fe2—Al3^vii	180.0
Al1^xix—Si1—Al1^viii	180.00 (4)	Al1^xii—Fe2—Al3^viii	61.58 (2)
Al1^xvii—Si1—Al1	114.37 (3)	Al1^viii—Fe2—Al3^viii	118.42 (2)
Al1^vii—Si1—Al1	65.63 (3)	Al1^v—Fe2—Al3^viii	115.33 (3)
Al1^xviii—Si1—Al1	180.0	Al1^iv—Fe2—Al3^viii	61.58 (2)
Al1^xix—Si1—Al1	114.37 (3)	Al1^vii—Fe2—Al3^viii	118.42 (2)
Al1^viii—Si1—Al1	65.63 (3)	Al1—Fe2—Al3^viii	64.67 (3)
Al1^xvii—Si1—Cr1^xiii	61.518 (11)	Al3^v—Fe2—Al3^viii	64.787 (18)
Al1^vii—Si1—Cr1^xiii	118.482 (11)	Al3^iv—Fe2—Al3^viii	64.787 (18)
Al1^xviii—Si1—Cr1^xiii	61.519 (11)	Al3^vii—Fe2—Al3^viii	115.213 (18)

Symmetry codes: (i) x−2/3, y−1/3, z−1/3; (ii) −x+y+1/3, −x+2/3, z−1/3; (iii) −x+1/3, −y+2/3, −z+2/3; (iv) x−y, x, −z+1; (v) −x, −y, −z+1; (vi) y−1/3, −x+y+1/3, −z+1/3; (vii) −x+y, −x, z; (viii) −y, x−y, z; (ix) −y+2/3, x−y+1/3, z+1/3; (x) y+1/3, −x+y+2/3, −z+2/3; (xi) −x+2/3, −y+1/3, −z+4/3; (xii) y, −x+y, −z+1; (xiii) x−y−1/3, x−2/3, −z+1/3; (xiv) −x+2/3, −y+1/3, −z+1/3; (xv) x−y+1/3, x−1/3, −z+2/3; (xvi) x+2/3, y+1/3, z+1/3; (xvii) x−y, x, −z; (xviii) −x, −y, −z; (xix) y, −x+y, −z; (xx) x−y+2/3, x+1/3, −z+1/3.

Funding information

Funding for this research was provided by: The National Natural Science Foundation of China (grant Nos. 52173231 and U23A20537); The Innovation Ability Promotion Project of Hebei supported by Hebei Key Lab for Optimizing Metal Product Technology and Performance (grant No. 22567609H).

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